一类混合型二阶非线性微分方程的振动性

OSCILLATION FOR A CLASS OF MIXED TYPE SECOND ORDER NONLINEAR DIFFERENTIAL

采用一种新的方法 ,研究了一类混合型二阶非线性微分方程x″(t) +p(t) |x(t) |αsgnx(t) +q(t) |x(t) |βsgnx(t) =0的振动性 ,其中t∈ [t0 ,∞ ) ,p(t) ,q(t)为定义在 [t0 ,∞ )上的实值连续函数 ,且允许变号 ,0 <α <1,β>1为常数 .

By applying a new method, the oscillation for a class of mixed second order nonlinear differentialequations x″(t)+p(t)|x(t)|~αsgn x(t)+q(t)|x(t)|~βsgn x(t)=0,0<α<1,β>1 is studied, where t∈[t 0,∞),p,q [JP2]are continuous on [t 0,∞) and their signs can be changed, what's more 0<α<1,β>1 are constants.[JP]